Question: $\lim_{x\to 0}\tan(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $-1$ (Choice B) B $0$ (Choice C) C $1$ (Choice D) D The limit doesn't exist.
Answer: $\tan(x)$ is continuous on all points in its domain. Therefore, if $x=0$ is within the domain of $\tan(x)$, we can find $\lim_{x\to 0}\tan(x)$ by direct substitution. $x=0$ is indeed in the domain of $\tan(x)$ : $\begin{aligned} \tan\left(0\right)&=\dfrac{\sin\left(0\right)}{\cos\left(0\right)} \\\\ &=\dfrac{0}{1} \\\\ &=0 \end{aligned}$ $\lim_{x\to 0}\tan(x)=0$